Решебник по алгебре 9 класс Макарычев Задание 216

 

\[\boxed{\text{216}\text{\ (216)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[2px^{2} - 2x - 2p - 3\]

\[x_{1} = 0:\ \]

\[2p \cdot 0^{2} - 2 \cdot 0 - 2p - 3 = 0\]

\[- 2p - 3 = 0\]

\[2p = - 3\]

\[p = - 1,5.\]

\[Подставим:\]

\[2 \cdot ( - 1,5)x^{2} - 2x - 2 \cdot\]

\[\cdot ( - 1,5) - 3 = 0\]

\[- 3x^{2} - 2x = 0\]

\[3x^{2} + 2x = 0\]

\[x(3x + 2) = 0\]

\[x_{1} = 0;\ \ x_{2} = - \frac{2}{3}.\]

\[Ответ:при\ p = - 1,5;\ \ \]

\[x = 0;\ \ x = - \frac{2}{3}.\]

\[\boxed{\text{216.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]

\[Пусть\ x - первое\ число,\ y -\]

\[второе\ число.\]

\[Составим\ систему\ уравнений:\]

\[\left\{ \begin{matrix} x = y + 5\ \ \ \ \ \ \ \ \ \ \ \\ x^{3} = y^{3} + 3185 \\ \end{matrix} \right.\ \Longrightarrow\]

\[\Longrightarrow (y + 5)^{3} = y^{3} + 3185\]

\[y^{2} + 5y - 204 = 0\]

\[D = 25 + 4 \cdot 204 = 841\]

\[y_{1,2} = \frac{- 5 \pm 29}{2},\ \ \]

\[y_{1} = 12;\ \ \ \ \ \ \ \ y_{2} = - 17;\]

\[y_{1} = 12 \Longrightarrow x_{1} = 12 + 5 = 17;\]

\[y_{2} = - 17 \Longrightarrow x_{2} = - 17 + 5 =\]

\[= - 12.\]

\[Ответ:12\ и\ 17\ или\ \ \ \]

\[( - 12)\ и\ ( - 17).\]